Finite Group Databasebeta

← D23×#355 #15675073

Subgroups — D23×#355 #15675073

Order 2944.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#124×D23C211yesmaximal, characteristic
2#101×D23C212yesmaximal, complemented
3#13092214C211yesmaximal, characteristic, complemented
4#13092213C212yesmaximal, complemented
5C23×#355C211yesmaximal, characteristic, complemented
6C2×Q8×D23C2211yescharacteristic
7C2×D4×D23C411yescharacteristic
8C23×#124C2211yescharacteristic
9#10625118C2211yescharacteristic
10#10625107C411yescharacteristic
11M16×D23—22no—
12#10625056—22no—
13C22⋊C4×D23—22no—
14#10625046C411yescharacteristic
15C42×D23C411yescharacteristic
16C23×#101C2212yescomplemented
17#10625018C2212yescomplemented
18#10625006—22no—
19C23×D23—21no—
20C2×Q8×C23C2311yescharacteristic
21C2×D4×C23C2×C411yescharacteristic
22C2×C22⋊D23—21no—
23Q8×D23—41no—
24Q8×D23—41no—
25D4×D23—41no—
26D4×D23—41no—
27C2×D92C2×C411yescharacteristic
28C2×C4×D23—21no—
29C2×C4×D23C2×C411yescharacteristic
30C2×C4×D23D412yes—
31C2×Dic46C2×C411yescharacteristic
32C2×Dic46D412yes—
33M16×C23—22no—
34C22⋊C4×C23—22no—
35C42×C23C2×C411yescharacteristic
36C22⋊Dic23—22no—
37(C2×D23)⋊C4—22no—
38(C2×D23)⋊C4—22no—
39C4×Dic23—21no—
40C4×Dic23C2×C411yescharacteristic
41#67267—22no—
42#67262—42no—
43C8×D23—42no—
44C23×C23—21no—
45C22×D23—21no—
46C22×D23—44no—
47C22×D23—41no—
48C22×D23—41no—
49C22×D23C22⋊C411yescharacteristic
50Q8×C23—41no—
51D4×C23—41no—
52C2×C4×C23—21no—
53C2×C4×C23C22×C411yescharacteristic
54C2×C4×C23C2×D412yes—
55C22⋊D23—42no—
56C2×Dic23—21no—
57C2×Dic23C22⋊C411yescharacteristic
58C2×Dic23C22⋊C412yes—
59D92—41no—
60C4×D23—22no—
61C4×D23—22no—
62C4×D23—21no—
63C4×D23—21no—
64C4×D23—42no—
65Dic46—41no—
66Dic46—42no—
67C8×C23—42no—
68C23⋊C8—42no—
69C2×#355—231nomaximal, Sylow
70C22×C23—42no—
71C22×C23—41no—
72C22×C23C2×C22⋊C411yescharacteristic
73C2×D23—22no—
74C2×D23—42no—
75C2×D23—41no—
76C2×D23—82no—
77C2×D23—82no—
78C2×D23#9911yescharacteristic
79C2×D23#9911yescharacteristic
80C4×C23—22no—
81C4×C23—21no—
82C4×C23—41no—
83Dic23—22no—
84Dic23—21no—
85Dic23—41no—
86C2×#124—231no—
87C2×#101—232no—
88#355—231no—
89#355—232no—
90#355D2311yescharacteristic, direct product factor
91C2×C23—21no—
92C2×C23—81no—
93C2×C23C2×#9911yescharacteristic
94D23—21no—
95D23—81no—
96D23#35512yesdirect product factor
97C22×Q8—231no—
98C22×D4—231no—
99C2×M16—462no—
100#124—231no—
101#124—231no—
102#124—231no—
103#124—462no—
104#124C2×D2311yescharacteristic
105C2×C22⋊C4—462no—
106C2×C42—231no—
107#101—232no—
108#101—462no—
109#101C2×D2312yescomplemented
110C23C2×#35511yescharacteristic, complemented, Sylow
111C24—461no—
112C2×Q8—231no—
113C2×Q8—232no—
114C2×Q8—921no—
115C2×Q8—921no—
116C2×Q8C22×D2311yescharacteristic
117C2×D4—231no—
118C2×D4—461no—
119C2×D4—921no—
120C2×D4—921no—
121C2×D4C4×D2311yescharacteristic
122C22×C4—231no—
123C22×C4—232no—
124C22×C4—461no—
125M16—22no—
126M16—462no—
127M16—922no—
128C2×C8—922no—
129C22⋊C4—22no—
130C22⋊C4—462no—
131C22⋊C4—462no—
132C22⋊C4—462no—
133C42—231no—
134C42—461no—
135C42C4×D2311yescharacteristic
136C23—21no—
137C23—231no—
138C23—461no—
139C23—921no—
140C23—921no—
141C23—924no—
142Q8—41no—
143Q8—922no—
144Q8—921no—
145D4—41no—
146D4—921no—
147D4—922no—
148C2×C4—21no—
149C2×C4—231no—
150C2×C4—232no—
151C2×C4—462no—
152C2×C4—462no—
153C2×C4—461no—
154C2×C4—461no—
155C2×C4—461no—
156C2×C4—922no—
157C2×C4C2×C4×D2311yescharacteristic
158C2×C4D4×D2312yes—
159C8—42no—
160C8—922no—
161C22—42no—
162C22—41no—
163C22—231no—
164C22—231no—
165C22—462no—
166C22—922no—
167C22—921no—
168C22—1842no—
169C22—1842no—
170C22C22⋊C4×D2311yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—461no—
175C4—462no—
176C4—921no—
177C2—21no—
178C2—81no—
179C2—232no—
180C2—461no—
181C2—1841no—
182C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC2×C4×C23C22×C4
FrattiniC2×Q8C22×D23
FittingC23×#355C2
socleC2×C23C2×#99
prime radicalC2×D4×D23C4
cosocleC2×Q8×C23C23
hypercenter#355D23
hypocenterC23C2×#355
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #101×D23C2semidirect
3. #13092214C2semidirect
4. #13092213C2semidirect
5. C23×#355C2semidirect
16. C23×#101C22semidirect
17. #10625018C22semidirect
90. #355D23direct (N × H)
96. D23#355direct (N × H)
109. #101C2×D23semidirect
110. C23C2×#355semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#124×D232
#101×D232
#130922142
#130922132
C23×#3552
C2×#35523